Monte Carlo evaluation of periodic error uncertainty

This paper presents a single analytical expression for the displacement recorded using a polarization-coded, heterodyne interferometer in terms of the various uncertainty contributors, including periodic error and other phase nonlinearities, Abbe error, cosine error, deadpath error, environmental error, interferometer thermal effects, and wavelength stability. The displacement equation is based on the periodic error expression reported by Cosijns et al. Monte Carlo simulation is applied to determine the first and second order periodic error uncertainty. The Monte Carlo simulation is then extended to include the other uncertainty contributors included in the analytical displacement equation.